I’m not exactly an economics expert, but I think your premise is a little backward. It’s not that the various schools “come to the same conclusion” but rather that the concept of price-controls being counter-intuitive is a fundamental concept of basic economics. Any introductory to macro textbook will likely address this in the first few chapters.
As far as I know, the various economic “schools” all agree on the basic core premises of economics that are covered in an Intro textbook. It isn’t until you start getting into the more complicated issues and the question of “well what should we do about it” that the various schools of thought begin to become distinct.